Question

A tape dispenser holds 1.14 x 10^4 mm of tape that is 12.7 mm wide. Multiply the two numbers to find the total area in square millimeters of tape. Write the product in scientific notation.

answers:

1.4478 x 10^5 mm^2

14.478 x 10^5 mm^2

1.4478 x 10^4 mm^2

14.478 x 10^4 mm^2

Answer 1

are you sure

Answer 2

To find the total area of the tape in square millimeters, we need to multiply the length of the tape by its width.

Given:
- Length of tape = \(1.14 \times 10^4\) mm
- Width of tape = 12.7 mm

Now, multiply these two values:

\[
\text{Area} = 1.14 \times 10^4 \text{ mm} \times 12.7 \text{ mm}
\]

First, calculate \(1.14 \times 12.7\):

\[
1.14 \times 12.7 = 14.478
\]

Next, we can combine this with the power of ten:

\[
\text{Area} = 14.478 \times 10^4 \text{ mm}^2
\]

Since scientific notation typically has a single non-zero digit to the left of the decimal, we should convert \(14.478\) to scientific notation:

\[
14.478 = 1.4478 \times 10^1
\]

So we adjust the area accordingly:

\[
\text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} \text{ mm}^2
\]

Therefore, the total area in scientific notation is:
\[
\boxed{1.4478 \times 10^5 \text{ mm}^2}
\]

Answer 3

Let’s verify the calculation step-by-step to ensure accuracy:

1. **Length of tape:** \( 1.14 \times 10^4 \) mm
2. **Width of tape:** \( 12.7 \) mm

Now, we multiply these two values to find the area:

\[
\text{Area} = \text{Length} \times \text{Width} = (1.14 \times 10^4) \times 12.7
\]

3. **Calculate \( 1.14 \times 12.7 \):**

\[
1.14 \times 12.7 = 14.478
\]

4. **Combine with the scientific notation for length:**

The length is in scientific notation, so:

\[
\text{Area} = 14.478 \times 10^4 \text{ mm}^2
\]

5. **Convert \( 14.478 \) into scientific notation:**

To convert \( 14.478 \) into scientific notation, we express it as:

\[
14.478 = 1.4478 \times 10^1
\]

6. **Combine it with \( 10^4 \):**

\[
\text{Area} = (1.4478 \times 10^1) \times 10^4 = 1.4478 \times 10^{5} \text{ mm}^2
\]

The calculation and conversion were executed correctly, confirming that the total area of tape is:

\[
\boxed{1.4478 \times 10^5 \text{ mm}^2}
\]

So, yes, the answer is indeed accurate. Thank you for prompting this verification!